Properties

Label 8002.2.a.d.1.20
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 1
Dimension 69
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-1.96349 q^{3}\) \(+1.00000 q^{4}\) \(+0.136598 q^{5}\) \(-1.96349 q^{6}\) \(-0.645165 q^{7}\) \(+1.00000 q^{8}\) \(+0.855285 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-1.96349 q^{3}\) \(+1.00000 q^{4}\) \(+0.136598 q^{5}\) \(-1.96349 q^{6}\) \(-0.645165 q^{7}\) \(+1.00000 q^{8}\) \(+0.855285 q^{9}\) \(+0.136598 q^{10}\) \(+5.43439 q^{11}\) \(-1.96349 q^{12}\) \(+2.62554 q^{13}\) \(-0.645165 q^{14}\) \(-0.268208 q^{15}\) \(+1.00000 q^{16}\) \(+0.137394 q^{17}\) \(+0.855285 q^{18}\) \(-3.70721 q^{19}\) \(+0.136598 q^{20}\) \(+1.26677 q^{21}\) \(+5.43439 q^{22}\) \(-7.68849 q^{23}\) \(-1.96349 q^{24}\) \(-4.98134 q^{25}\) \(+2.62554 q^{26}\) \(+4.21112 q^{27}\) \(-0.645165 q^{28}\) \(-5.85445 q^{29}\) \(-0.268208 q^{30}\) \(+7.74561 q^{31}\) \(+1.00000 q^{32}\) \(-10.6704 q^{33}\) \(+0.137394 q^{34}\) \(-0.0881280 q^{35}\) \(+0.855285 q^{36}\) \(-8.38418 q^{37}\) \(-3.70721 q^{38}\) \(-5.15522 q^{39}\) \(+0.136598 q^{40}\) \(+7.12279 q^{41}\) \(+1.26677 q^{42}\) \(-9.80190 q^{43}\) \(+5.43439 q^{44}\) \(+0.116830 q^{45}\) \(-7.68849 q^{46}\) \(-7.62943 q^{47}\) \(-1.96349 q^{48}\) \(-6.58376 q^{49}\) \(-4.98134 q^{50}\) \(-0.269772 q^{51}\) \(+2.62554 q^{52}\) \(+6.45470 q^{53}\) \(+4.21112 q^{54}\) \(+0.742324 q^{55}\) \(-0.645165 q^{56}\) \(+7.27906 q^{57}\) \(-5.85445 q^{58}\) \(+10.6054 q^{59}\) \(-0.268208 q^{60}\) \(+10.8817 q^{61}\) \(+7.74561 q^{62}\) \(-0.551800 q^{63}\) \(+1.00000 q^{64}\) \(+0.358642 q^{65}\) \(-10.6704 q^{66}\) \(-10.7922 q^{67}\) \(+0.137394 q^{68}\) \(+15.0963 q^{69}\) \(-0.0881280 q^{70}\) \(+7.43766 q^{71}\) \(+0.855285 q^{72}\) \(-2.53878 q^{73}\) \(-8.38418 q^{74}\) \(+9.78080 q^{75}\) \(-3.70721 q^{76}\) \(-3.50608 q^{77}\) \(-5.15522 q^{78}\) \(+1.30045 q^{79}\) \(+0.136598 q^{80}\) \(-10.8343 q^{81}\) \(+7.12279 q^{82}\) \(-17.2760 q^{83}\) \(+1.26677 q^{84}\) \(+0.0187677 q^{85}\) \(-9.80190 q^{86}\) \(+11.4951 q^{87}\) \(+5.43439 q^{88}\) \(-10.7479 q^{89}\) \(+0.116830 q^{90}\) \(-1.69391 q^{91}\) \(-7.68849 q^{92}\) \(-15.2084 q^{93}\) \(-7.62943 q^{94}\) \(-0.506395 q^{95}\) \(-1.96349 q^{96}\) \(-1.49348 q^{97}\) \(-6.58376 q^{98}\) \(+4.64795 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −1.96349 −1.13362 −0.566810 0.823848i \(-0.691823\pi\)
−0.566810 + 0.823848i \(0.691823\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.136598 0.0610883 0.0305441 0.999533i \(-0.490276\pi\)
0.0305441 + 0.999533i \(0.490276\pi\)
\(6\) −1.96349 −0.801591
\(7\) −0.645165 −0.243850 −0.121925 0.992539i \(-0.538907\pi\)
−0.121925 + 0.992539i \(0.538907\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.855285 0.285095
\(10\) 0.136598 0.0431959
\(11\) 5.43439 1.63853 0.819265 0.573415i \(-0.194382\pi\)
0.819265 + 0.573415i \(0.194382\pi\)
\(12\) −1.96349 −0.566810
\(13\) 2.62554 0.728194 0.364097 0.931361i \(-0.381378\pi\)
0.364097 + 0.931361i \(0.381378\pi\)
\(14\) −0.645165 −0.172428
\(15\) −0.268208 −0.0692509
\(16\) 1.00000 0.250000
\(17\) 0.137394 0.0333230 0.0166615 0.999861i \(-0.494696\pi\)
0.0166615 + 0.999861i \(0.494696\pi\)
\(18\) 0.855285 0.201593
\(19\) −3.70721 −0.850492 −0.425246 0.905078i \(-0.639812\pi\)
−0.425246 + 0.905078i \(0.639812\pi\)
\(20\) 0.136598 0.0305441
\(21\) 1.26677 0.276433
\(22\) 5.43439 1.15862
\(23\) −7.68849 −1.60316 −0.801580 0.597887i \(-0.796007\pi\)
−0.801580 + 0.597887i \(0.796007\pi\)
\(24\) −1.96349 −0.400795
\(25\) −4.98134 −0.996268
\(26\) 2.62554 0.514911
\(27\) 4.21112 0.810431
\(28\) −0.645165 −0.121925
\(29\) −5.85445 −1.08714 −0.543572 0.839362i \(-0.682929\pi\)
−0.543572 + 0.839362i \(0.682929\pi\)
\(30\) −0.268208 −0.0489678
\(31\) 7.74561 1.39115 0.695576 0.718452i \(-0.255149\pi\)
0.695576 + 0.718452i \(0.255149\pi\)
\(32\) 1.00000 0.176777
\(33\) −10.6704 −1.85747
\(34\) 0.137394 0.0235629
\(35\) −0.0881280 −0.0148963
\(36\) 0.855285 0.142547
\(37\) −8.38418 −1.37835 −0.689175 0.724595i \(-0.742027\pi\)
−0.689175 + 0.724595i \(0.742027\pi\)
\(38\) −3.70721 −0.601389
\(39\) −5.15522 −0.825496
\(40\) 0.136598 0.0215980
\(41\) 7.12279 1.11239 0.556197 0.831051i \(-0.312260\pi\)
0.556197 + 0.831051i \(0.312260\pi\)
\(42\) 1.26677 0.195468
\(43\) −9.80190 −1.49478 −0.747388 0.664388i \(-0.768692\pi\)
−0.747388 + 0.664388i \(0.768692\pi\)
\(44\) 5.43439 0.819265
\(45\) 0.116830 0.0174160
\(46\) −7.68849 −1.13361
\(47\) −7.62943 −1.11287 −0.556433 0.830892i \(-0.687831\pi\)
−0.556433 + 0.830892i \(0.687831\pi\)
\(48\) −1.96349 −0.283405
\(49\) −6.58376 −0.940537
\(50\) −4.98134 −0.704468
\(51\) −0.269772 −0.0377757
\(52\) 2.62554 0.364097
\(53\) 6.45470 0.886621 0.443311 0.896368i \(-0.353804\pi\)
0.443311 + 0.896368i \(0.353804\pi\)
\(54\) 4.21112 0.573061
\(55\) 0.742324 0.100095
\(56\) −0.645165 −0.0862138
\(57\) 7.27906 0.964135
\(58\) −5.85445 −0.768727
\(59\) 10.6054 1.38070 0.690351 0.723475i \(-0.257456\pi\)
0.690351 + 0.723475i \(0.257456\pi\)
\(60\) −0.268208 −0.0346254
\(61\) 10.8817 1.39325 0.696627 0.717434i \(-0.254683\pi\)
0.696627 + 0.717434i \(0.254683\pi\)
\(62\) 7.74561 0.983693
\(63\) −0.551800 −0.0695203
\(64\) 1.00000 0.125000
\(65\) 0.358642 0.0444841
\(66\) −10.6704 −1.31343
\(67\) −10.7922 −1.31848 −0.659240 0.751933i \(-0.729122\pi\)
−0.659240 + 0.751933i \(0.729122\pi\)
\(68\) 0.137394 0.0166615
\(69\) 15.0963 1.81738
\(70\) −0.0881280 −0.0105333
\(71\) 7.43766 0.882687 0.441344 0.897338i \(-0.354502\pi\)
0.441344 + 0.897338i \(0.354502\pi\)
\(72\) 0.855285 0.100796
\(73\) −2.53878 −0.297141 −0.148571 0.988902i \(-0.547467\pi\)
−0.148571 + 0.988902i \(0.547467\pi\)
\(74\) −8.38418 −0.974641
\(75\) 9.78080 1.12939
\(76\) −3.70721 −0.425246
\(77\) −3.50608 −0.399555
\(78\) −5.15522 −0.583714
\(79\) 1.30045 0.146312 0.0731559 0.997321i \(-0.476693\pi\)
0.0731559 + 0.997321i \(0.476693\pi\)
\(80\) 0.136598 0.0152721
\(81\) −10.8343 −1.20382
\(82\) 7.12279 0.786581
\(83\) −17.2760 −1.89629 −0.948146 0.317834i \(-0.897044\pi\)
−0.948146 + 0.317834i \(0.897044\pi\)
\(84\) 1.26677 0.138216
\(85\) 0.0187677 0.00203565
\(86\) −9.80190 −1.05697
\(87\) 11.4951 1.23241
\(88\) 5.43439 0.579308
\(89\) −10.7479 −1.13927 −0.569635 0.821898i \(-0.692916\pi\)
−0.569635 + 0.821898i \(0.692916\pi\)
\(90\) 0.116830 0.0123149
\(91\) −1.69391 −0.177570
\(92\) −7.68849 −0.801580
\(93\) −15.2084 −1.57704
\(94\) −7.62943 −0.786916
\(95\) −0.506395 −0.0519551
\(96\) −1.96349 −0.200398
\(97\) −1.49348 −0.151640 −0.0758198 0.997122i \(-0.524157\pi\)
−0.0758198 + 0.997122i \(0.524157\pi\)
\(98\) −6.58376 −0.665060
\(99\) 4.64795 0.467137
\(100\) −4.98134 −0.498134
\(101\) −0.169838 −0.0168995 −0.00844974 0.999964i \(-0.502690\pi\)
−0.00844974 + 0.999964i \(0.502690\pi\)
\(102\) −0.269772 −0.0267114
\(103\) −8.97453 −0.884286 −0.442143 0.896944i \(-0.645782\pi\)
−0.442143 + 0.896944i \(0.645782\pi\)
\(104\) 2.62554 0.257456
\(105\) 0.173038 0.0168868
\(106\) 6.45470 0.626936
\(107\) 16.3362 1.57928 0.789638 0.613573i \(-0.210268\pi\)
0.789638 + 0.613573i \(0.210268\pi\)
\(108\) 4.21112 0.405215
\(109\) −2.81281 −0.269418 −0.134709 0.990885i \(-0.543010\pi\)
−0.134709 + 0.990885i \(0.543010\pi\)
\(110\) 0.742324 0.0707778
\(111\) 16.4622 1.56253
\(112\) −0.645165 −0.0609624
\(113\) 2.96629 0.279045 0.139523 0.990219i \(-0.455443\pi\)
0.139523 + 0.990219i \(0.455443\pi\)
\(114\) 7.27906 0.681746
\(115\) −1.05023 −0.0979343
\(116\) −5.85445 −0.543572
\(117\) 2.24559 0.207604
\(118\) 10.6054 0.976303
\(119\) −0.0886421 −0.00812581
\(120\) −0.268208 −0.0244839
\(121\) 18.5326 1.68478
\(122\) 10.8817 0.985179
\(123\) −13.9855 −1.26103
\(124\) 7.74561 0.695576
\(125\) −1.36343 −0.121949
\(126\) −0.551800 −0.0491583
\(127\) 8.58178 0.761509 0.380755 0.924676i \(-0.375664\pi\)
0.380755 + 0.924676i \(0.375664\pi\)
\(128\) 1.00000 0.0883883
\(129\) 19.2459 1.69451
\(130\) 0.358642 0.0314550
\(131\) 18.2274 1.59254 0.796269 0.604943i \(-0.206804\pi\)
0.796269 + 0.604943i \(0.206804\pi\)
\(132\) −10.6704 −0.928735
\(133\) 2.39176 0.207392
\(134\) −10.7922 −0.932306
\(135\) 0.575229 0.0495078
\(136\) 0.137394 0.0117815
\(137\) 2.28829 0.195502 0.0977509 0.995211i \(-0.468835\pi\)
0.0977509 + 0.995211i \(0.468835\pi\)
\(138\) 15.0963 1.28508
\(139\) −4.39175 −0.372503 −0.186252 0.982502i \(-0.559634\pi\)
−0.186252 + 0.982502i \(0.559634\pi\)
\(140\) −0.0881280 −0.00744817
\(141\) 14.9803 1.26157
\(142\) 7.43766 0.624154
\(143\) 14.2682 1.19317
\(144\) 0.855285 0.0712737
\(145\) −0.799704 −0.0664118
\(146\) −2.53878 −0.210111
\(147\) 12.9271 1.06621
\(148\) −8.38418 −0.689175
\(149\) 16.2633 1.33234 0.666172 0.745798i \(-0.267932\pi\)
0.666172 + 0.745798i \(0.267932\pi\)
\(150\) 9.78080 0.798599
\(151\) −6.30411 −0.513021 −0.256511 0.966541i \(-0.582573\pi\)
−0.256511 + 0.966541i \(0.582573\pi\)
\(152\) −3.70721 −0.300694
\(153\) 0.117511 0.00950023
\(154\) −3.50608 −0.282528
\(155\) 1.05803 0.0849831
\(156\) −5.15522 −0.412748
\(157\) 8.71210 0.695301 0.347651 0.937624i \(-0.386980\pi\)
0.347651 + 0.937624i \(0.386980\pi\)
\(158\) 1.30045 0.103458
\(159\) −12.6737 −1.00509
\(160\) 0.136598 0.0107990
\(161\) 4.96035 0.390930
\(162\) −10.8343 −0.851226
\(163\) −13.7071 −1.07362 −0.536810 0.843703i \(-0.680371\pi\)
−0.536810 + 0.843703i \(0.680371\pi\)
\(164\) 7.12279 0.556197
\(165\) −1.45754 −0.113470
\(166\) −17.2760 −1.34088
\(167\) −22.8476 −1.76800 −0.883999 0.467489i \(-0.845159\pi\)
−0.883999 + 0.467489i \(0.845159\pi\)
\(168\) 1.26677 0.0977338
\(169\) −6.10653 −0.469733
\(170\) 0.0187677 0.00143942
\(171\) −3.17072 −0.242471
\(172\) −9.80190 −0.747388
\(173\) −13.7361 −1.04433 −0.522167 0.852843i \(-0.674876\pi\)
−0.522167 + 0.852843i \(0.674876\pi\)
\(174\) 11.4951 0.871445
\(175\) 3.21379 0.242940
\(176\) 5.43439 0.409632
\(177\) −20.8235 −1.56519
\(178\) −10.7479 −0.805586
\(179\) 0.228136 0.0170517 0.00852585 0.999964i \(-0.497286\pi\)
0.00852585 + 0.999964i \(0.497286\pi\)
\(180\) 0.116830 0.00870798
\(181\) −23.6984 −1.76149 −0.880745 0.473592i \(-0.842957\pi\)
−0.880745 + 0.473592i \(0.842957\pi\)
\(182\) −1.69391 −0.125561
\(183\) −21.3660 −1.57942
\(184\) −7.68849 −0.566803
\(185\) −1.14526 −0.0842010
\(186\) −15.2084 −1.11513
\(187\) 0.746655 0.0546008
\(188\) −7.62943 −0.556433
\(189\) −2.71687 −0.197623
\(190\) −0.506395 −0.0367378
\(191\) −19.4428 −1.40683 −0.703417 0.710777i \(-0.748343\pi\)
−0.703417 + 0.710777i \(0.748343\pi\)
\(192\) −1.96349 −0.141703
\(193\) −9.37529 −0.674848 −0.337424 0.941353i \(-0.609556\pi\)
−0.337424 + 0.941353i \(0.609556\pi\)
\(194\) −1.49348 −0.107225
\(195\) −0.704190 −0.0504281
\(196\) −6.58376 −0.470269
\(197\) −14.8784 −1.06004 −0.530021 0.847984i \(-0.677816\pi\)
−0.530021 + 0.847984i \(0.677816\pi\)
\(198\) 4.64795 0.330315
\(199\) 17.5989 1.24756 0.623778 0.781602i \(-0.285597\pi\)
0.623778 + 0.781602i \(0.285597\pi\)
\(200\) −4.98134 −0.352234
\(201\) 21.1904 1.49466
\(202\) −0.169838 −0.0119497
\(203\) 3.77709 0.265100
\(204\) −0.269772 −0.0188878
\(205\) 0.972956 0.0679542
\(206\) −8.97453 −0.625285
\(207\) −6.57585 −0.457053
\(208\) 2.62554 0.182049
\(209\) −20.1464 −1.39356
\(210\) 0.173038 0.0119408
\(211\) 24.7428 1.70336 0.851682 0.524059i \(-0.175583\pi\)
0.851682 + 0.524059i \(0.175583\pi\)
\(212\) 6.45470 0.443311
\(213\) −14.6037 −1.00063
\(214\) 16.3362 1.11672
\(215\) −1.33891 −0.0913132
\(216\) 4.21112 0.286531
\(217\) −4.99720 −0.339232
\(218\) −2.81281 −0.190507
\(219\) 4.98486 0.336846
\(220\) 0.742324 0.0500475
\(221\) 0.360735 0.0242656
\(222\) 16.4622 1.10487
\(223\) −11.6833 −0.782374 −0.391187 0.920311i \(-0.627935\pi\)
−0.391187 + 0.920311i \(0.627935\pi\)
\(224\) −0.645165 −0.0431069
\(225\) −4.26046 −0.284031
\(226\) 2.96629 0.197315
\(227\) 14.3672 0.953582 0.476791 0.879017i \(-0.341800\pi\)
0.476791 + 0.879017i \(0.341800\pi\)
\(228\) 7.27906 0.482067
\(229\) −9.27281 −0.612764 −0.306382 0.951909i \(-0.599119\pi\)
−0.306382 + 0.951909i \(0.599119\pi\)
\(230\) −1.05023 −0.0692500
\(231\) 6.88414 0.452943
\(232\) −5.85445 −0.384364
\(233\) 28.5096 1.86772 0.933861 0.357635i \(-0.116417\pi\)
0.933861 + 0.357635i \(0.116417\pi\)
\(234\) 2.24559 0.146799
\(235\) −1.04216 −0.0679831
\(236\) 10.6054 0.690351
\(237\) −2.55341 −0.165862
\(238\) −0.0886421 −0.00574581
\(239\) −1.92886 −0.124767 −0.0623837 0.998052i \(-0.519870\pi\)
−0.0623837 + 0.998052i \(0.519870\pi\)
\(240\) −0.268208 −0.0173127
\(241\) −17.7798 −1.14530 −0.572650 0.819800i \(-0.694084\pi\)
−0.572650 + 0.819800i \(0.694084\pi\)
\(242\) 18.5326 1.19132
\(243\) 8.63973 0.554239
\(244\) 10.8817 0.696627
\(245\) −0.899325 −0.0574558
\(246\) −13.9855 −0.891684
\(247\) −9.73343 −0.619323
\(248\) 7.74561 0.491847
\(249\) 33.9213 2.14968
\(250\) −1.36343 −0.0862307
\(251\) −21.1878 −1.33736 −0.668680 0.743551i \(-0.733140\pi\)
−0.668680 + 0.743551i \(0.733140\pi\)
\(252\) −0.551800 −0.0347601
\(253\) −41.7822 −2.62683
\(254\) 8.58178 0.538469
\(255\) −0.0368502 −0.00230765
\(256\) 1.00000 0.0625000
\(257\) −27.9902 −1.74598 −0.872990 0.487738i \(-0.837822\pi\)
−0.872990 + 0.487738i \(0.837822\pi\)
\(258\) 19.2459 1.19820
\(259\) 5.40918 0.336110
\(260\) 0.358642 0.0222421
\(261\) −5.00722 −0.309939
\(262\) 18.2274 1.12609
\(263\) −23.4759 −1.44758 −0.723792 0.690018i \(-0.757602\pi\)
−0.723792 + 0.690018i \(0.757602\pi\)
\(264\) −10.6704 −0.656715
\(265\) 0.881696 0.0541621
\(266\) 2.39176 0.146648
\(267\) 21.1033 1.29150
\(268\) −10.7922 −0.659240
\(269\) −19.9201 −1.21455 −0.607275 0.794492i \(-0.707737\pi\)
−0.607275 + 0.794492i \(0.707737\pi\)
\(270\) 0.575229 0.0350073
\(271\) −12.7918 −0.777046 −0.388523 0.921439i \(-0.627015\pi\)
−0.388523 + 0.921439i \(0.627015\pi\)
\(272\) 0.137394 0.00833076
\(273\) 3.32597 0.201297
\(274\) 2.28829 0.138241
\(275\) −27.0705 −1.63242
\(276\) 15.0963 0.908688
\(277\) 18.8469 1.13240 0.566201 0.824267i \(-0.308413\pi\)
0.566201 + 0.824267i \(0.308413\pi\)
\(278\) −4.39175 −0.263400
\(279\) 6.62470 0.396611
\(280\) −0.0881280 −0.00526665
\(281\) −12.9456 −0.772268 −0.386134 0.922443i \(-0.626190\pi\)
−0.386134 + 0.922443i \(0.626190\pi\)
\(282\) 14.9803 0.892063
\(283\) −17.4489 −1.03723 −0.518614 0.855009i \(-0.673552\pi\)
−0.518614 + 0.855009i \(0.673552\pi\)
\(284\) 7.43766 0.441344
\(285\) 0.994301 0.0588973
\(286\) 14.2682 0.843697
\(287\) −4.59538 −0.271257
\(288\) 0.855285 0.0503981
\(289\) −16.9811 −0.998890
\(290\) −0.799704 −0.0469602
\(291\) 2.93242 0.171902
\(292\) −2.53878 −0.148571
\(293\) −12.8542 −0.750950 −0.375475 0.926833i \(-0.622520\pi\)
−0.375475 + 0.926833i \(0.622520\pi\)
\(294\) 12.9271 0.753926
\(295\) 1.44867 0.0843447
\(296\) −8.38418 −0.487320
\(297\) 22.8849 1.32792
\(298\) 16.2633 0.942109
\(299\) −20.1865 −1.16741
\(300\) 9.78080 0.564695
\(301\) 6.32385 0.364500
\(302\) −6.30411 −0.362761
\(303\) 0.333474 0.0191576
\(304\) −3.70721 −0.212623
\(305\) 1.48641 0.0851114
\(306\) 0.117511 0.00671768
\(307\) 25.2718 1.44234 0.721168 0.692760i \(-0.243606\pi\)
0.721168 + 0.692760i \(0.243606\pi\)
\(308\) −3.50608 −0.199777
\(309\) 17.6214 1.00244
\(310\) 1.05803 0.0600921
\(311\) 8.91856 0.505725 0.252862 0.967502i \(-0.418628\pi\)
0.252862 + 0.967502i \(0.418628\pi\)
\(312\) −5.15522 −0.291857
\(313\) −28.9112 −1.63416 −0.817079 0.576526i \(-0.804408\pi\)
−0.817079 + 0.576526i \(0.804408\pi\)
\(314\) 8.71210 0.491652
\(315\) −0.0753745 −0.00424687
\(316\) 1.30045 0.0731559
\(317\) −14.6613 −0.823458 −0.411729 0.911306i \(-0.635075\pi\)
−0.411729 + 0.911306i \(0.635075\pi\)
\(318\) −12.6737 −0.710707
\(319\) −31.8154 −1.78132
\(320\) 0.136598 0.00763603
\(321\) −32.0758 −1.79030
\(322\) 4.96035 0.276429
\(323\) −0.509350 −0.0283410
\(324\) −10.8343 −0.601908
\(325\) −13.0787 −0.725477
\(326\) −13.7071 −0.759165
\(327\) 5.52291 0.305418
\(328\) 7.12279 0.393290
\(329\) 4.92224 0.271372
\(330\) −1.45754 −0.0802352
\(331\) 6.90707 0.379647 0.189824 0.981818i \(-0.439208\pi\)
0.189824 + 0.981818i \(0.439208\pi\)
\(332\) −17.2760 −0.948146
\(333\) −7.17086 −0.392961
\(334\) −22.8476 −1.25016
\(335\) −1.47419 −0.0805436
\(336\) 1.26677 0.0691082
\(337\) 18.4880 1.00711 0.503554 0.863964i \(-0.332026\pi\)
0.503554 + 0.863964i \(0.332026\pi\)
\(338\) −6.10653 −0.332151
\(339\) −5.82428 −0.316331
\(340\) 0.0187677 0.00101782
\(341\) 42.0927 2.27945
\(342\) −3.17072 −0.171453
\(343\) 8.76377 0.473199
\(344\) −9.80190 −0.528483
\(345\) 2.06211 0.111020
\(346\) −13.7361 −0.738455
\(347\) 8.90909 0.478265 0.239132 0.970987i \(-0.423137\pi\)
0.239132 + 0.970987i \(0.423137\pi\)
\(348\) 11.4951 0.616205
\(349\) 6.31107 0.337824 0.168912 0.985631i \(-0.445975\pi\)
0.168912 + 0.985631i \(0.445975\pi\)
\(350\) 3.21379 0.171784
\(351\) 11.0565 0.590151
\(352\) 5.43439 0.289654
\(353\) 3.99399 0.212579 0.106289 0.994335i \(-0.466103\pi\)
0.106289 + 0.994335i \(0.466103\pi\)
\(354\) −20.8235 −1.10676
\(355\) 1.01597 0.0539218
\(356\) −10.7479 −0.569635
\(357\) 0.174048 0.00921158
\(358\) 0.228136 0.0120574
\(359\) 21.0913 1.11316 0.556579 0.830795i \(-0.312114\pi\)
0.556579 + 0.830795i \(0.312114\pi\)
\(360\) 0.116830 0.00615747
\(361\) −5.25661 −0.276664
\(362\) −23.6984 −1.24556
\(363\) −36.3885 −1.90990
\(364\) −1.69391 −0.0887849
\(365\) −0.346791 −0.0181519
\(366\) −21.3660 −1.11682
\(367\) 7.10645 0.370954 0.185477 0.982649i \(-0.440617\pi\)
0.185477 + 0.982649i \(0.440617\pi\)
\(368\) −7.68849 −0.400790
\(369\) 6.09201 0.317138
\(370\) −1.14526 −0.0595391
\(371\) −4.16435 −0.216202
\(372\) −15.2084 −0.788519
\(373\) −20.1340 −1.04250 −0.521249 0.853404i \(-0.674534\pi\)
−0.521249 + 0.853404i \(0.674534\pi\)
\(374\) 0.746655 0.0386086
\(375\) 2.67707 0.138243
\(376\) −7.62943 −0.393458
\(377\) −15.3711 −0.791652
\(378\) −2.71687 −0.139741
\(379\) −15.6170 −0.802190 −0.401095 0.916037i \(-0.631370\pi\)
−0.401095 + 0.916037i \(0.631370\pi\)
\(380\) −0.506395 −0.0259775
\(381\) −16.8502 −0.863263
\(382\) −19.4428 −0.994782
\(383\) −23.6516 −1.20854 −0.604270 0.796779i \(-0.706535\pi\)
−0.604270 + 0.796779i \(0.706535\pi\)
\(384\) −1.96349 −0.100199
\(385\) −0.478922 −0.0244081
\(386\) −9.37529 −0.477190
\(387\) −8.38341 −0.426153
\(388\) −1.49348 −0.0758198
\(389\) −5.10491 −0.258829 −0.129415 0.991591i \(-0.541310\pi\)
−0.129415 + 0.991591i \(0.541310\pi\)
\(390\) −0.704190 −0.0356581
\(391\) −1.05636 −0.0534222
\(392\) −6.58376 −0.332530
\(393\) −35.7893 −1.80533
\(394\) −14.8784 −0.749564
\(395\) 0.177638 0.00893793
\(396\) 4.64795 0.233568
\(397\) 39.6218 1.98856 0.994281 0.106792i \(-0.0340580\pi\)
0.994281 + 0.106792i \(0.0340580\pi\)
\(398\) 17.5989 0.882155
\(399\) −4.69620 −0.235104
\(400\) −4.98134 −0.249067
\(401\) −25.0412 −1.25050 −0.625248 0.780426i \(-0.715002\pi\)
−0.625248 + 0.780426i \(0.715002\pi\)
\(402\) 21.1904 1.05688
\(403\) 20.3364 1.01303
\(404\) −0.169838 −0.00844974
\(405\) −1.47994 −0.0735390
\(406\) 3.77709 0.187454
\(407\) −45.5629 −2.25847
\(408\) −0.269772 −0.0133557
\(409\) 30.8092 1.52342 0.761708 0.647920i \(-0.224361\pi\)
0.761708 + 0.647920i \(0.224361\pi\)
\(410\) 0.972956 0.0480508
\(411\) −4.49303 −0.221625
\(412\) −8.97453 −0.442143
\(413\) −6.84222 −0.336683
\(414\) −6.57585 −0.323185
\(415\) −2.35986 −0.115841
\(416\) 2.62554 0.128728
\(417\) 8.62314 0.422277
\(418\) −20.1464 −0.985393
\(419\) 23.2766 1.13714 0.568568 0.822636i \(-0.307498\pi\)
0.568568 + 0.822636i \(0.307498\pi\)
\(420\) 0.173038 0.00844340
\(421\) −16.6580 −0.811859 −0.405930 0.913904i \(-0.633052\pi\)
−0.405930 + 0.913904i \(0.633052\pi\)
\(422\) 24.7428 1.20446
\(423\) −6.52533 −0.317273
\(424\) 6.45470 0.313468
\(425\) −0.684408 −0.0331987
\(426\) −14.6037 −0.707554
\(427\) −7.02047 −0.339744
\(428\) 16.3362 0.789638
\(429\) −28.0155 −1.35260
\(430\) −1.33891 −0.0645682
\(431\) 3.10680 0.149649 0.0748246 0.997197i \(-0.476160\pi\)
0.0748246 + 0.997197i \(0.476160\pi\)
\(432\) 4.21112 0.202608
\(433\) −17.9951 −0.864789 −0.432395 0.901684i \(-0.642331\pi\)
−0.432395 + 0.901684i \(0.642331\pi\)
\(434\) −4.99720 −0.239873
\(435\) 1.57021 0.0752857
\(436\) −2.81281 −0.134709
\(437\) 28.5028 1.36348
\(438\) 4.98486 0.238186
\(439\) 18.1319 0.865386 0.432693 0.901541i \(-0.357563\pi\)
0.432693 + 0.901541i \(0.357563\pi\)
\(440\) 0.742324 0.0353889
\(441\) −5.63099 −0.268142
\(442\) 0.360735 0.0171584
\(443\) −1.65471 −0.0786178 −0.0393089 0.999227i \(-0.512516\pi\)
−0.0393089 + 0.999227i \(0.512516\pi\)
\(444\) 16.4622 0.781263
\(445\) −1.46813 −0.0695961
\(446\) −11.6833 −0.553222
\(447\) −31.9329 −1.51037
\(448\) −0.645165 −0.0304812
\(449\) 4.02871 0.190126 0.0950632 0.995471i \(-0.469695\pi\)
0.0950632 + 0.995471i \(0.469695\pi\)
\(450\) −4.26046 −0.200840
\(451\) 38.7080 1.82269
\(452\) 2.96629 0.139523
\(453\) 12.3780 0.581571
\(454\) 14.3672 0.674284
\(455\) −0.231384 −0.0108474
\(456\) 7.27906 0.340873
\(457\) −9.73886 −0.455565 −0.227782 0.973712i \(-0.573147\pi\)
−0.227782 + 0.973712i \(0.573147\pi\)
\(458\) −9.27281 −0.433290
\(459\) 0.578585 0.0270060
\(460\) −1.05023 −0.0489672
\(461\) 7.82597 0.364492 0.182246 0.983253i \(-0.441663\pi\)
0.182246 + 0.983253i \(0.441663\pi\)
\(462\) 6.88414 0.320279
\(463\) 7.98347 0.371023 0.185512 0.982642i \(-0.440606\pi\)
0.185512 + 0.982642i \(0.440606\pi\)
\(464\) −5.85445 −0.271786
\(465\) −2.07743 −0.0963386
\(466\) 28.5096 1.32068
\(467\) 12.9077 0.597295 0.298648 0.954363i \(-0.403464\pi\)
0.298648 + 0.954363i \(0.403464\pi\)
\(468\) 2.24559 0.103802
\(469\) 6.96277 0.321511
\(470\) −1.04216 −0.0480713
\(471\) −17.1061 −0.788208
\(472\) 10.6054 0.488152
\(473\) −53.2673 −2.44923
\(474\) −2.55341 −0.117282
\(475\) 18.4669 0.847318
\(476\) −0.0886421 −0.00406290
\(477\) 5.52061 0.252771
\(478\) −1.92886 −0.0882238
\(479\) −1.55841 −0.0712058 −0.0356029 0.999366i \(-0.511335\pi\)
−0.0356029 + 0.999366i \(0.511335\pi\)
\(480\) −0.268208 −0.0122419
\(481\) −22.0130 −1.00371
\(482\) −17.7798 −0.809849
\(483\) −9.73958 −0.443166
\(484\) 18.5326 0.842390
\(485\) −0.204005 −0.00926340
\(486\) 8.63973 0.391906
\(487\) −9.52027 −0.431405 −0.215702 0.976459i \(-0.569204\pi\)
−0.215702 + 0.976459i \(0.569204\pi\)
\(488\) 10.8817 0.492589
\(489\) 26.9137 1.21708
\(490\) −0.899325 −0.0406274
\(491\) −21.3348 −0.962825 −0.481413 0.876494i \(-0.659876\pi\)
−0.481413 + 0.876494i \(0.659876\pi\)
\(492\) −13.9855 −0.630516
\(493\) −0.804369 −0.0362270
\(494\) −9.73343 −0.437928
\(495\) 0.634898 0.0285366
\(496\) 7.74561 0.347788
\(497\) −4.79852 −0.215243
\(498\) 33.9213 1.52005
\(499\) 8.70138 0.389527 0.194764 0.980850i \(-0.437606\pi\)
0.194764 + 0.980850i \(0.437606\pi\)
\(500\) −1.36343 −0.0609743
\(501\) 44.8609 2.00424
\(502\) −21.1878 −0.945656
\(503\) 39.1479 1.74552 0.872758 0.488152i \(-0.162329\pi\)
0.872758 + 0.488152i \(0.162329\pi\)
\(504\) −0.551800 −0.0245791
\(505\) −0.0231994 −0.00103236
\(506\) −41.7822 −1.85745
\(507\) 11.9901 0.532499
\(508\) 8.58178 0.380755
\(509\) −30.7906 −1.36477 −0.682384 0.730994i \(-0.739057\pi\)
−0.682384 + 0.730994i \(0.739057\pi\)
\(510\) −0.0368502 −0.00163175
\(511\) 1.63793 0.0724578
\(512\) 1.00000 0.0441942
\(513\) −15.6115 −0.689265
\(514\) −27.9902 −1.23459
\(515\) −1.22590 −0.0540195
\(516\) 19.2459 0.847254
\(517\) −41.4613 −1.82347
\(518\) 5.40918 0.237666
\(519\) 26.9706 1.18388
\(520\) 0.358642 0.0157275
\(521\) −21.1470 −0.926467 −0.463233 0.886236i \(-0.653311\pi\)
−0.463233 + 0.886236i \(0.653311\pi\)
\(522\) −5.00722 −0.219160
\(523\) −9.33978 −0.408400 −0.204200 0.978929i \(-0.565459\pi\)
−0.204200 + 0.978929i \(0.565459\pi\)
\(524\) 18.2274 0.796269
\(525\) −6.31024 −0.275401
\(526\) −23.4759 −1.02360
\(527\) 1.06420 0.0463574
\(528\) −10.6704 −0.464368
\(529\) 36.1129 1.57013
\(530\) 0.881696 0.0382984
\(531\) 9.07061 0.393631
\(532\) 2.39176 0.103696
\(533\) 18.7012 0.810038
\(534\) 21.1033 0.913229
\(535\) 2.23148 0.0964752
\(536\) −10.7922 −0.466153
\(537\) −0.447943 −0.0193301
\(538\) −19.9201 −0.858817
\(539\) −35.7787 −1.54110
\(540\) 0.575229 0.0247539
\(541\) −21.1622 −0.909836 −0.454918 0.890533i \(-0.650331\pi\)
−0.454918 + 0.890533i \(0.650331\pi\)
\(542\) −12.7918 −0.549455
\(543\) 46.5315 1.99686
\(544\) 0.137394 0.00589074
\(545\) −0.384222 −0.0164583
\(546\) 3.32597 0.142338
\(547\) −43.1738 −1.84598 −0.922989 0.384825i \(-0.874262\pi\)
−0.922989 + 0.384825i \(0.874262\pi\)
\(548\) 2.28829 0.0977509
\(549\) 9.30691 0.397209
\(550\) −27.0705 −1.15429
\(551\) 21.7037 0.924608
\(552\) 15.0963 0.642539
\(553\) −0.839004 −0.0356781
\(554\) 18.8469 0.800729
\(555\) 2.24870 0.0954520
\(556\) −4.39175 −0.186252
\(557\) −2.08548 −0.0883647 −0.0441823 0.999023i \(-0.514068\pi\)
−0.0441823 + 0.999023i \(0.514068\pi\)
\(558\) 6.62470 0.280446
\(559\) −25.7353 −1.08849
\(560\) −0.0881280 −0.00372409
\(561\) −1.46605 −0.0618966
\(562\) −12.9456 −0.546076
\(563\) 34.2456 1.44328 0.721640 0.692268i \(-0.243389\pi\)
0.721640 + 0.692268i \(0.243389\pi\)
\(564\) 14.9803 0.630784
\(565\) 0.405188 0.0170464
\(566\) −17.4489 −0.733431
\(567\) 6.98994 0.293550
\(568\) 7.43766 0.312077
\(569\) −16.2887 −0.682857 −0.341429 0.939908i \(-0.610911\pi\)
−0.341429 + 0.939908i \(0.610911\pi\)
\(570\) 0.994301 0.0416467
\(571\) 29.0341 1.21504 0.607519 0.794305i \(-0.292165\pi\)
0.607519 + 0.794305i \(0.292165\pi\)
\(572\) 14.2682 0.596584
\(573\) 38.1758 1.59482
\(574\) −4.59538 −0.191807
\(575\) 38.2990 1.59718
\(576\) 0.855285 0.0356369
\(577\) −24.9873 −1.04024 −0.520118 0.854094i \(-0.674112\pi\)
−0.520118 + 0.854094i \(0.674112\pi\)
\(578\) −16.9811 −0.706322
\(579\) 18.4083 0.765021
\(580\) −0.799704 −0.0332059
\(581\) 11.1459 0.462410
\(582\) 2.93242 0.121553
\(583\) 35.0773 1.45276
\(584\) −2.53878 −0.105055
\(585\) 0.306741 0.0126822
\(586\) −12.8542 −0.531002
\(587\) −2.00171 −0.0826195 −0.0413098 0.999146i \(-0.513153\pi\)
−0.0413098 + 0.999146i \(0.513153\pi\)
\(588\) 12.9271 0.533106
\(589\) −28.7146 −1.18316
\(590\) 1.44867 0.0596407
\(591\) 29.2136 1.20169
\(592\) −8.38418 −0.344587
\(593\) −17.5875 −0.722232 −0.361116 0.932521i \(-0.617604\pi\)
−0.361116 + 0.932521i \(0.617604\pi\)
\(594\) 22.8849 0.938978
\(595\) −0.0121083 −0.000496391 0
\(596\) 16.2633 0.666172
\(597\) −34.5553 −1.41425
\(598\) −20.1865 −0.825485
\(599\) 20.2843 0.828792 0.414396 0.910097i \(-0.363993\pi\)
0.414396 + 0.910097i \(0.363993\pi\)
\(600\) 9.78080 0.399300
\(601\) −43.8527 −1.78879 −0.894394 0.447280i \(-0.852393\pi\)
−0.894394 + 0.447280i \(0.852393\pi\)
\(602\) 6.32385 0.257741
\(603\) −9.23042 −0.375892
\(604\) −6.30411 −0.256511
\(605\) 2.53150 0.102920
\(606\) 0.333474 0.0135465
\(607\) −5.40321 −0.219310 −0.109655 0.993970i \(-0.534975\pi\)
−0.109655 + 0.993970i \(0.534975\pi\)
\(608\) −3.70721 −0.150347
\(609\) −7.41627 −0.300522
\(610\) 1.48641 0.0601829
\(611\) −20.0314 −0.810383
\(612\) 0.117511 0.00475011
\(613\) 12.0452 0.486501 0.243250 0.969964i \(-0.421786\pi\)
0.243250 + 0.969964i \(0.421786\pi\)
\(614\) 25.2718 1.01989
\(615\) −1.91039 −0.0770342
\(616\) −3.50608 −0.141264
\(617\) 35.5498 1.43118 0.715590 0.698520i \(-0.246158\pi\)
0.715590 + 0.698520i \(0.246158\pi\)
\(618\) 17.6214 0.708836
\(619\) −27.4798 −1.10450 −0.552252 0.833677i \(-0.686231\pi\)
−0.552252 + 0.833677i \(0.686231\pi\)
\(620\) 1.05803 0.0424915
\(621\) −32.3772 −1.29925
\(622\) 8.91856 0.357602
\(623\) 6.93415 0.277811
\(624\) −5.15522 −0.206374
\(625\) 24.7205 0.988819
\(626\) −28.9112 −1.15552
\(627\) 39.5572 1.57976
\(628\) 8.71210 0.347651
\(629\) −1.15194 −0.0459308
\(630\) −0.0753745 −0.00300299
\(631\) −16.5309 −0.658083 −0.329042 0.944315i \(-0.606726\pi\)
−0.329042 + 0.944315i \(0.606726\pi\)
\(632\) 1.30045 0.0517290
\(633\) −48.5822 −1.93097
\(634\) −14.6613 −0.582273
\(635\) 1.17225 0.0465193
\(636\) −12.6737 −0.502546
\(637\) −17.2859 −0.684894
\(638\) −31.8154 −1.25958
\(639\) 6.36131 0.251650
\(640\) 0.136598 0.00539949
\(641\) 18.7497 0.740571 0.370285 0.928918i \(-0.379260\pi\)
0.370285 + 0.928918i \(0.379260\pi\)
\(642\) −32.0758 −1.26593
\(643\) 22.6413 0.892884 0.446442 0.894812i \(-0.352691\pi\)
0.446442 + 0.894812i \(0.352691\pi\)
\(644\) 4.96035 0.195465
\(645\) 2.62894 0.103515
\(646\) −0.509350 −0.0200401
\(647\) 7.68801 0.302247 0.151123 0.988515i \(-0.451711\pi\)
0.151123 + 0.988515i \(0.451711\pi\)
\(648\) −10.8343 −0.425613
\(649\) 57.6337 2.26232
\(650\) −13.0787 −0.512990
\(651\) 9.81194 0.384560
\(652\) −13.7071 −0.536810
\(653\) 12.3860 0.484703 0.242351 0.970189i \(-0.422081\pi\)
0.242351 + 0.970189i \(0.422081\pi\)
\(654\) 5.52291 0.215963
\(655\) 2.48982 0.0972853
\(656\) 7.12279 0.278098
\(657\) −2.17138 −0.0847135
\(658\) 4.92224 0.191889
\(659\) 47.4180 1.84714 0.923571 0.383427i \(-0.125256\pi\)
0.923571 + 0.383427i \(0.125256\pi\)
\(660\) −1.45754 −0.0567348
\(661\) −12.0229 −0.467638 −0.233819 0.972280i \(-0.575122\pi\)
−0.233819 + 0.972280i \(0.575122\pi\)
\(662\) 6.90707 0.268451
\(663\) −0.708298 −0.0275080
\(664\) −17.2760 −0.670441
\(665\) 0.326709 0.0126692
\(666\) −7.17086 −0.277865
\(667\) 45.0119 1.74287
\(668\) −22.8476 −0.883999
\(669\) 22.9401 0.886915
\(670\) −1.47419 −0.0569530
\(671\) 59.1351 2.28289
\(672\) 1.26677 0.0488669
\(673\) −35.4126 −1.36506 −0.682528 0.730860i \(-0.739119\pi\)
−0.682528 + 0.730860i \(0.739119\pi\)
\(674\) 18.4880 0.712132
\(675\) −20.9770 −0.807407
\(676\) −6.10653 −0.234867
\(677\) 28.9929 1.11429 0.557144 0.830416i \(-0.311897\pi\)
0.557144 + 0.830416i \(0.311897\pi\)
\(678\) −5.82428 −0.223680
\(679\) 0.963539 0.0369772
\(680\) 0.0187677 0.000719710 0
\(681\) −28.2098 −1.08100
\(682\) 42.0927 1.61181
\(683\) −31.8393 −1.21830 −0.609148 0.793056i \(-0.708489\pi\)
−0.609148 + 0.793056i \(0.708489\pi\)
\(684\) −3.17072 −0.121235
\(685\) 0.312575 0.0119429
\(686\) 8.76377 0.334602
\(687\) 18.2070 0.694642
\(688\) −9.80190 −0.373694
\(689\) 16.9471 0.645632
\(690\) 2.06211 0.0785032
\(691\) 18.3672 0.698722 0.349361 0.936988i \(-0.386399\pi\)
0.349361 + 0.936988i \(0.386399\pi\)
\(692\) −13.7361 −0.522167
\(693\) −2.99870 −0.113911
\(694\) 8.90909 0.338184
\(695\) −0.599902 −0.0227556
\(696\) 11.4951 0.435722
\(697\) 0.978632 0.0370683
\(698\) 6.31107 0.238878
\(699\) −55.9782 −2.11729
\(700\) 3.21379 0.121470
\(701\) 42.7075 1.61304 0.806520 0.591207i \(-0.201348\pi\)
0.806520 + 0.591207i \(0.201348\pi\)
\(702\) 11.0565 0.417300
\(703\) 31.0819 1.17228
\(704\) 5.43439 0.204816
\(705\) 2.04627 0.0770670
\(706\) 3.99399 0.150316
\(707\) 0.109573 0.00412093
\(708\) −20.8235 −0.782596
\(709\) −51.1452 −1.92080 −0.960398 0.278630i \(-0.910120\pi\)
−0.960398 + 0.278630i \(0.910120\pi\)
\(710\) 1.01597 0.0381285
\(711\) 1.11225 0.0417127
\(712\) −10.7479 −0.402793
\(713\) −59.5520 −2.23024
\(714\) 0.174048 0.00651357
\(715\) 1.94900 0.0728886
\(716\) 0.228136 0.00852585
\(717\) 3.78729 0.141439
\(718\) 21.0913 0.787121
\(719\) −15.9336 −0.594222 −0.297111 0.954843i \(-0.596023\pi\)
−0.297111 + 0.954843i \(0.596023\pi\)
\(720\) 0.116830 0.00435399
\(721\) 5.79005 0.215633
\(722\) −5.25661 −0.195631
\(723\) 34.9105 1.29833
\(724\) −23.6984 −0.880745
\(725\) 29.1630 1.08309
\(726\) −36.3885 −1.35050
\(727\) −45.3193 −1.68080 −0.840400 0.541967i \(-0.817680\pi\)
−0.840400 + 0.541967i \(0.817680\pi\)
\(728\) −1.69391 −0.0627804
\(729\) 15.5390 0.575519
\(730\) −0.346791 −0.0128353
\(731\) −1.34673 −0.0498105
\(732\) −21.3660 −0.789710
\(733\) −32.3169 −1.19365 −0.596826 0.802371i \(-0.703572\pi\)
−0.596826 + 0.802371i \(0.703572\pi\)
\(734\) 7.10645 0.262304
\(735\) 1.76581 0.0651331
\(736\) −7.68849 −0.283401
\(737\) −58.6491 −2.16037
\(738\) 6.09201 0.224250
\(739\) 19.0615 0.701187 0.350594 0.936528i \(-0.385980\pi\)
0.350594 + 0.936528i \(0.385980\pi\)
\(740\) −1.14526 −0.0421005
\(741\) 19.1115 0.702077
\(742\) −4.16435 −0.152878
\(743\) 50.4184 1.84967 0.924836 0.380366i \(-0.124202\pi\)
0.924836 + 0.380366i \(0.124202\pi\)
\(744\) −15.2084 −0.557567
\(745\) 2.22153 0.0813906
\(746\) −20.1340 −0.737158
\(747\) −14.7759 −0.540623
\(748\) 0.746655 0.0273004
\(749\) −10.5395 −0.385106
\(750\) 2.67707 0.0977528
\(751\) 19.2912 0.703945 0.351973 0.936010i \(-0.385511\pi\)
0.351973 + 0.936010i \(0.385511\pi\)
\(752\) −7.62943 −0.278217
\(753\) 41.6019 1.51606
\(754\) −15.3711 −0.559783
\(755\) −0.861125 −0.0313396
\(756\) −2.71687 −0.0988116
\(757\) −22.6521 −0.823303 −0.411651 0.911341i \(-0.635048\pi\)
−0.411651 + 0.911341i \(0.635048\pi\)
\(758\) −15.6170 −0.567234
\(759\) 82.0389 2.97782
\(760\) −0.506395 −0.0183689
\(761\) −30.1840 −1.09417 −0.547084 0.837078i \(-0.684262\pi\)
−0.547084 + 0.837078i \(0.684262\pi\)
\(762\) −16.8502 −0.610419
\(763\) 1.81472 0.0656974
\(764\) −19.4428 −0.703417
\(765\) 0.0160518 0.000580352 0
\(766\) −23.6516 −0.854567
\(767\) 27.8448 1.00542
\(768\) −1.96349 −0.0708513
\(769\) −36.8802 −1.32993 −0.664967 0.746872i \(-0.731555\pi\)
−0.664967 + 0.746872i \(0.731555\pi\)
\(770\) −0.478922 −0.0172591
\(771\) 54.9584 1.97928
\(772\) −9.37529 −0.337424
\(773\) 5.77620 0.207755 0.103878 0.994590i \(-0.466875\pi\)
0.103878 + 0.994590i \(0.466875\pi\)
\(774\) −8.38341 −0.301336
\(775\) −38.5835 −1.38596
\(776\) −1.49348 −0.0536127
\(777\) −10.6209 −0.381021
\(778\) −5.10491 −0.183020
\(779\) −26.4057 −0.946081
\(780\) −0.704190 −0.0252141
\(781\) 40.4191 1.44631
\(782\) −1.05636 −0.0377752
\(783\) −24.6538 −0.881055
\(784\) −6.58376 −0.235134
\(785\) 1.19005 0.0424748
\(786\) −35.7893 −1.27656
\(787\) 6.57884 0.234510 0.117255 0.993102i \(-0.462590\pi\)
0.117255 + 0.993102i \(0.462590\pi\)
\(788\) −14.8784 −0.530021
\(789\) 46.0946 1.64101
\(790\) 0.177638 0.00632007
\(791\) −1.91375 −0.0680451
\(792\) 4.64795 0.165158
\(793\) 28.5702 1.01456
\(794\) 39.6218 1.40613
\(795\) −1.73120 −0.0613993
\(796\) 17.5989 0.623778
\(797\) 50.0108 1.77147 0.885737 0.464187i \(-0.153653\pi\)
0.885737 + 0.464187i \(0.153653\pi\)
\(798\) −4.69620 −0.166244
\(799\) −1.04824 −0.0370841
\(800\) −4.98134 −0.176117
\(801\) −9.19248 −0.324800
\(802\) −25.0412 −0.884234
\(803\) −13.7967 −0.486875
\(804\) 21.1904 0.747328
\(805\) 0.677571 0.0238812
\(806\) 20.3364 0.716320
\(807\) 39.1129 1.37684
\(808\) −0.169838 −0.00597487
\(809\) 22.4710 0.790037 0.395018 0.918673i \(-0.370738\pi\)
0.395018 + 0.918673i \(0.370738\pi\)
\(810\) −1.47994 −0.0519999
\(811\) −29.1457 −1.02345 −0.511723 0.859151i \(-0.670992\pi\)
−0.511723 + 0.859151i \(0.670992\pi\)
\(812\) 3.77709 0.132550
\(813\) 25.1165 0.880875
\(814\) −45.5629 −1.59698
\(815\) −1.87235 −0.0655856
\(816\) −0.269772 −0.00944392
\(817\) 36.3377 1.27129
\(818\) 30.8092 1.07722
\(819\) −1.44877 −0.0506243
\(820\) 0.972956 0.0339771
\(821\) −20.1165 −0.702072 −0.351036 0.936362i \(-0.614171\pi\)
−0.351036 + 0.936362i \(0.614171\pi\)
\(822\) −4.49303 −0.156712
\(823\) 20.9550 0.730445 0.365223 0.930920i \(-0.380993\pi\)
0.365223 + 0.930920i \(0.380993\pi\)
\(824\) −8.97453 −0.312642
\(825\) 53.1527 1.85054
\(826\) −6.84222 −0.238071
\(827\) 33.8858 1.17832 0.589162 0.808015i \(-0.299458\pi\)
0.589162 + 0.808015i \(0.299458\pi\)
\(828\) −6.57585 −0.228527
\(829\) 10.9601 0.380659 0.190329 0.981720i \(-0.439044\pi\)
0.190329 + 0.981720i \(0.439044\pi\)
\(830\) −2.35986 −0.0819121
\(831\) −37.0057 −1.28371
\(832\) 2.62554 0.0910243
\(833\) −0.904572 −0.0313416
\(834\) 8.62314 0.298595
\(835\) −3.12092 −0.108004
\(836\) −20.1464 −0.696778
\(837\) 32.6177 1.12743
\(838\) 23.2766 0.804076
\(839\) −2.45946 −0.0849100 −0.0424550 0.999098i \(-0.513518\pi\)
−0.0424550 + 0.999098i \(0.513518\pi\)
\(840\) 0.173038 0.00597039
\(841\) 5.27461 0.181883
\(842\) −16.6580 −0.574071
\(843\) 25.4185 0.875459
\(844\) 24.7428 0.851682
\(845\) −0.834137 −0.0286952
\(846\) −6.52533 −0.224346
\(847\) −11.9566 −0.410833
\(848\) 6.45470 0.221655
\(849\) 34.2606 1.17582
\(850\) −0.684408 −0.0234750
\(851\) 64.4616 2.20972
\(852\) −14.6037 −0.500316
\(853\) −20.7983 −0.712120 −0.356060 0.934463i \(-0.615880\pi\)
−0.356060 + 0.934463i \(0.615880\pi\)
\(854\) −7.02047 −0.240235
\(855\) −0.433112 −0.0148121
\(856\) 16.3362 0.558358
\(857\) −45.4291 −1.55183 −0.775914 0.630839i \(-0.782711\pi\)
−0.775914 + 0.630839i \(0.782711\pi\)
\(858\) −28.0155 −0.956432
\(859\) −2.75793 −0.0940993 −0.0470496 0.998893i \(-0.514982\pi\)
−0.0470496 + 0.998893i \(0.514982\pi\)
\(860\) −1.33891 −0.0456566
\(861\) 9.02297 0.307502
\(862\) 3.10680 0.105818
\(863\) −38.5720 −1.31301 −0.656503 0.754323i \(-0.727965\pi\)
−0.656503 + 0.754323i \(0.727965\pi\)
\(864\) 4.21112 0.143265
\(865\) −1.87631 −0.0637965
\(866\) −17.9951 −0.611498
\(867\) 33.3422 1.13236
\(868\) −4.99720 −0.169616
\(869\) 7.06714 0.239736
\(870\) 1.57021 0.0532350
\(871\) −28.3354 −0.960110
\(872\) −2.81281 −0.0952536
\(873\) −1.27735 −0.0432317
\(874\) 28.5028 0.964123
\(875\) 0.879635 0.0297371
\(876\) 4.98486 0.168423
\(877\) 25.9340 0.875730 0.437865 0.899041i \(-0.355735\pi\)
0.437865 + 0.899041i \(0.355735\pi\)
\(878\) 18.1319 0.611920
\(879\) 25.2390 0.851292
\(880\) 0.742324 0.0250237
\(881\) 32.2921 1.08795 0.543974 0.839102i \(-0.316919\pi\)
0.543974 + 0.839102i \(0.316919\pi\)
\(882\) −5.63099 −0.189605
\(883\) −47.8695 −1.61094 −0.805468 0.592639i \(-0.798086\pi\)
−0.805468 + 0.592639i \(0.798086\pi\)
\(884\) 0.360735 0.0121328
\(885\) −2.84444 −0.0956148
\(886\) −1.65471 −0.0555912
\(887\) 40.6247 1.36405 0.682023 0.731331i \(-0.261101\pi\)
0.682023 + 0.731331i \(0.261101\pi\)
\(888\) 16.4622 0.552436
\(889\) −5.53666 −0.185694
\(890\) −1.46813 −0.0492118
\(891\) −58.8780 −1.97249
\(892\) −11.6833 −0.391187
\(893\) 28.2839 0.946484
\(894\) −31.9329 −1.06799
\(895\) 0.0311628 0.00104166
\(896\) −0.645165 −0.0215535
\(897\) 39.6359 1.32340
\(898\) 4.02871 0.134440
\(899\) −45.3463 −1.51238
\(900\) −4.26046 −0.142015
\(901\) 0.886839 0.0295449
\(902\) 38.7080 1.28884
\(903\) −12.4168 −0.413205
\(904\) 2.96629 0.0986574
\(905\) −3.23714 −0.107606
\(906\) 12.3780 0.411233
\(907\) 13.6558 0.453433 0.226717 0.973961i \(-0.427201\pi\)
0.226717 + 0.973961i \(0.427201\pi\)
\(908\) 14.3672 0.476791
\(909\) −0.145260 −0.00481796
\(910\) −0.231384 −0.00767030
\(911\) −47.1056 −1.56068 −0.780339 0.625357i \(-0.784953\pi\)
−0.780339 + 0.625357i \(0.784953\pi\)
\(912\) 7.27906 0.241034
\(913\) −93.8848 −3.10713
\(914\) −9.73886 −0.322133
\(915\) −2.91854 −0.0964840
\(916\) −9.27281 −0.306382
\(917\) −11.7597 −0.388340
\(918\) 0.578585 0.0190961
\(919\) 25.9098 0.854685 0.427342 0.904090i \(-0.359450\pi\)
0.427342 + 0.904090i \(0.359450\pi\)
\(920\) −1.05023 −0.0346250
\(921\) −49.6208 −1.63506
\(922\) 7.82597 0.257735
\(923\) 19.5279 0.642768
\(924\) 6.88414 0.226472
\(925\) 41.7644 1.37321
\(926\) 7.98347 0.262353
\(927\) −7.67578 −0.252106
\(928\) −5.85445 −0.192182
\(929\) −26.8377 −0.880515 −0.440257 0.897872i \(-0.645113\pi\)
−0.440257 + 0.897872i \(0.645113\pi\)
\(930\) −2.07743 −0.0681217
\(931\) 24.4074 0.799919
\(932\) 28.5096 0.933861
\(933\) −17.5115 −0.573300
\(934\) 12.9077 0.422352
\(935\) 0.101991 0.00333547
\(936\) 2.24559 0.0733993
\(937\) 43.3481 1.41612 0.708060 0.706153i \(-0.249571\pi\)
0.708060 + 0.706153i \(0.249571\pi\)
\(938\) 6.96277 0.227342
\(939\) 56.7668 1.85251
\(940\) −1.04216 −0.0339915
\(941\) −57.9078 −1.88774 −0.943871 0.330315i \(-0.892845\pi\)
−0.943871 + 0.330315i \(0.892845\pi\)
\(942\) −17.1061 −0.557347
\(943\) −54.7635 −1.78335
\(944\) 10.6054 0.345175
\(945\) −0.371118 −0.0120725
\(946\) −53.2673 −1.73187
\(947\) −30.9144 −1.00458 −0.502292 0.864698i \(-0.667510\pi\)
−0.502292 + 0.864698i \(0.667510\pi\)
\(948\) −2.55341 −0.0829310
\(949\) −6.66567 −0.216377
\(950\) 18.4669 0.599144
\(951\) 28.7872 0.933489
\(952\) −0.0886421 −0.00287291
\(953\) 41.9830 1.35996 0.679982 0.733229i \(-0.261988\pi\)
0.679982 + 0.733229i \(0.261988\pi\)
\(954\) 5.52061 0.178736
\(955\) −2.65584 −0.0859411
\(956\) −1.92886 −0.0623837
\(957\) 62.4691 2.01934
\(958\) −1.55841 −0.0503501
\(959\) −1.47633 −0.0476730
\(960\) −0.268208 −0.00865636
\(961\) 28.9945 0.935306
\(962\) −22.0130 −0.709728
\(963\) 13.9721 0.450243
\(964\) −17.7798 −0.572650
\(965\) −1.28064 −0.0412253
\(966\) −9.73958 −0.313366
\(967\) −7.22172 −0.232235 −0.116117 0.993235i \(-0.537045\pi\)
−0.116117 + 0.993235i \(0.537045\pi\)
\(968\) 18.5326 0.595660
\(969\) 1.00010 0.0321279
\(970\) −0.204005 −0.00655021
\(971\) −8.26287 −0.265168 −0.132584 0.991172i \(-0.542327\pi\)
−0.132584 + 0.991172i \(0.542327\pi\)
\(972\) 8.63973 0.277120
\(973\) 2.83340 0.0908348
\(974\) −9.52027 −0.305049
\(975\) 25.6799 0.822415
\(976\) 10.8817 0.348313
\(977\) −8.27305 −0.264678 −0.132339 0.991204i \(-0.542249\pi\)
−0.132339 + 0.991204i \(0.542249\pi\)
\(978\) 26.9137 0.860604
\(979\) −58.4080 −1.86673
\(980\) −0.899325 −0.0287279
\(981\) −2.40575 −0.0768097
\(982\) −21.3348 −0.680820
\(983\) −16.8305 −0.536810 −0.268405 0.963306i \(-0.586497\pi\)
−0.268405 + 0.963306i \(0.586497\pi\)
\(984\) −13.9855 −0.445842
\(985\) −2.03235 −0.0647562
\(986\) −0.804369 −0.0256163
\(987\) −9.66477 −0.307633
\(988\) −9.73343 −0.309662
\(989\) 75.3618 2.39637
\(990\) 0.634898 0.0201784
\(991\) 27.6418 0.878071 0.439036 0.898470i \(-0.355320\pi\)
0.439036 + 0.898470i \(0.355320\pi\)
\(992\) 7.74561 0.245923
\(993\) −13.5620 −0.430376
\(994\) −4.79852 −0.152200
\(995\) 2.40397 0.0762110
\(996\) 33.9213 1.07484
\(997\) 23.4908 0.743960 0.371980 0.928241i \(-0.378679\pi\)
0.371980 + 0.928241i \(0.378679\pi\)
\(998\) 8.70138 0.275437
\(999\) −35.3068 −1.11706
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))